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Hi,let:
0->A-> B -> 0
; A,B Z-modules, be a short exact sequence. It follows A is isomorphic with B.
. We have that tensor product is
right-exact , so that, for a ring R:
0-> A(x)R-> B(x)R ->0
is also exact. STILL: are A(x)R , B(x)R isomorphic?
I suspect no, if R has torsion. Anyone have an example of
A(x)R , B(x)R non-isomorphic, but A,B isomorphic? Thanks.
0->A-> B -> 0
; A,B Z-modules, be a short exact sequence. It follows A is isomorphic with B.
. We have that tensor product is
right-exact , so that, for a ring R:
0-> A(x)R-> B(x)R ->0
is also exact. STILL: are A(x)R , B(x)R isomorphic?
I suspect no, if R has torsion. Anyone have an example of
A(x)R , B(x)R non-isomorphic, but A,B isomorphic? Thanks.